Sampling from Boltzmann distributions is a fundamental problem in physics, chemistry, and biology. We introduce WAsserstein SAmpling via Bridge Interpolants (WASABI), a method that trains a diffusion model to generate samples from a target Boltzmann distribution given access only to the energy function. WASABI minimizes the KL divergence between the distribution generated by its diffusion model and the Boltzmann target using Wasserstein gradient flows. This approach builds on a principle underlying classical sampling methods such as Langevin dynamics. However, applying Wasserstein gradient flows to diffusion models is challenging because the updates require the gradient of the model's own log density, which is generally intractable. We derive a practical training algorithm that avoids computing this gradient. Once trained, WASABI can generate new samples without further evaluations of the energy or its gradient. On alanine dipeptide, WASABI outperforms the best reported baselines using an estimated 3.3 times fewer energy evaluations. It also achieves competitive performance on interacting particle system benchmarks.

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